Magnetic assembly of transparent and conducting graphene-based functional composites

Innovative methods producing transparent and flexible electrodes are highly sought in modern optoelectronic applications to replace metal oxides, but available solutions suffer from drawbacks such as brittleness, unaffordability and inadequate processability. Here we propose a general, simple strategy to produce hierarchical composites of functionalized graphene in polymeric matrices, exhibiting transparency and electron conductivity. These are obtained through protein-assisted functionalization of graphene with magnetic nanoparticles, followed by magnetic-directed assembly of the graphene within polymeric matrices undergoing sol–gel transitions. By applying rotating magnetic fields or magnetic moulds, both graphene orientation and distribution can be controlled within the composite. Importantly, by using magnetic virtual moulds of predefined meshes, graphene assembly is directed into double-percolating networks, reducing the percolation threshold and enabling combined optical transparency and electrical conductivity not accessible in single-network materials. The resulting composites open new possibilities on the quest of transparent electrodes for photovoltaics, organic light-emitting diodes and stretchable optoelectronic devices.


Raman characterization of reduced graphene oxide
A drop of respectively GO and of m-rGO suspensions was deposited on a glass slide and dried at 80 °C for 2 h. Each sample was analysed by using a confocal Moreover, the position of the G band is slightly shifted from 1566 cm -1 for the GO to 1578 cm -1 for m-rGO, thus approaching the value of natural graphite, 1581 cm -1 10 .

Wide and Small Angle X-ray Scattering (WAXS/SAXS) of aligned composite gelatin films
The multiple building blocks present in the composite lead to several scattering peaks for samples with horizontally or vertically-aligned m-rGO flakes. The large diffusive halo from the helical pitch or mean distance between neighboring peptide chains in gelatin is present in both spectra as the peak p-I at 4.6 (q= 1.36 -1 ) (see

Synthesis of graphene oxide (GO)
Graphene oxide was prepared following a documented protocol 11 . A mixture of 3.7 g of graphite powder (99.5% purity, Graphit Kropfmühl) and 120 mL of concentrated sulphuric acid (98.5%) was prepared and stirred in an ice bath.
Oxidation took place after addition of 2.5 g of NaNO 3 followed by 11.6 g of KMnO 4 .
The temperature was carefully kept under 20 °C to counteract the exothermic reaction. The mixture was then continuously stirred for 7 hours at 35 °C before further addition of 9.

Optical characterization and transparency measurements
Optical microscopy images were taken either with a small inverted microscope (Leica DMIL LED, Camera Leica DFC295, Switzerland, Fig. 3a and 4a, Fig. 2c) or a camera ( Fig. 2d and 3c, main manuscript). The profile plot of the striated gelatin composite film was extracted using ImageJ (Image J 1.47v).
The transparency of the composites was calculated as the ratio of the grey value of the whole image of the composite film, I 2 , divided by the average grey value of the polymer matrix, I 1 . The grey values were extracted using ImageJ. According to Paine et al 12 a material is said to be highly transparent if it shows a transparency of 90% or more at 100 nm thickness. Using the Beer Lambert law (Supplementary Equation 1 in the following) relating the incident light I 0 and transmitted light I 1 , this would mean that a film is defined as "optically transparent" if (1) where x is the 100 nm thickness and a 1 is the attenuation coefficient of the material, in the present case, the native gelatin. By applying the supplementary equation 1, this would mean that an attenuation coefficient a 1 inferior to 10 -3 nm -1 is required to have a transparent material.
We now take the measured I 1 as the reference system (gelatin), to detect what is the reduction in transparency after producing double percolation grids. After confining graphene in double percolating networks, the light I 2 which goes through a sample of thickness x is: where a 2 is now the attenuation coefficient of the meshed gelatin containing the double percolating network. Taking for I 2 /I 1 the value of 0.85 measured for our 30 µm thick film, leads to an attenuation coefficient a 2 of 5×10 -6 nm -1 which is at least three orders of magnitude lower than the value of 10 -3 nm -1 used above to define transparency.
We then have for the true transparency of the final material: (3) The new attenuation coefficient of the whole composite film is therefore a 1 + a 2 , but while a 1 is intrinsic to the continuous matrix, a 2 is typical of the procedure followed here. In other terms, it is a 2 , which quantifies the relative transparency between the original material and the same material after modification with the double percolating mesh network. We further note that a 1 can be chosen to be virtually equal to 0 (using a 100% transparent polymer), making relative transparency equivalent to true transparency.

Determination of m-rGO density
The volume fraction of m-rGO within the dried composite gelatin film was calculated by extrapolating the densities of m-rGO-gelatin composites of known composition to 100% m-rGO (Supplementary Figure 6). The densities were measured using the Archimedes principle and hexane (96%, Mutlisolvent, Scharlau, Spain) as a solvent. This revealed that the density of the m-rGO, !"#$ , is 2.3 g.cm -3 .
Additionally, given the known amount of 10 nm spherical iron oxide particles and BSA adsorbed to the rGO and their respective densities of 5.24 and 1.22 g.cm -3 , the iron oxide nanoparticles and BSA coating can be estimated to represent 40.9 vol% and 2.13 vol% of the total volume of the modified flakes, respectively. Therefore the volume fraction in rGO within the final dried gelatin composite film was calculated based on the initial amount of m-rGO, m mrGO. :

Measurement of the local conductivity
The prepared gelatin-mrGO composite films were always thoroughly dried under 0.02 mbar (using Bal-Tec SCD 050 Sputter Coater under Argon flow) prior to electrical conductivity measurements. Macroscopic 2-points probe measurements were performed using a handheld/portable digital multimeter (Voltcraft VC230) while microscopic 2-points probe measurements were done using a Hall effect measurement system of Accent HL5510PC (cleanroom facility FIRST). The resulting conductivity was calculated with: where d = 1 mm is the distance between the electrodes, l = 250 µm is the average diameter of each electrode and t = 30 µm is the thickness of the composite film.

Measurement of the global conductivity
Masks with openings defining the geometry of the electrodes were prepared and taped onto the samples (Supplementary Figure 7). The electrodes were made by sputtering 37.5 nm of Au/Pd on the specimen surface. The resistance R between the electrodes was measured using a handheld digital multimeter. The resulting conductivity was calculated with: where L = 900 µm is the distance between the electrodes, W = 1190 µm is the width of each electrode and t = 30 µm is the thickness of the composite film.

Variation of the electrical conductivity with applied strain
The gelatin m-rGO composite films were coated by a 3 mm-thick layer of polydimethylsiloxane (PDMS, Sylgard 184 Silicone Elastomer kit, Dow Corning, Michigan, USA) and cured for 1 hour at 100 °C. No high vacuum was applied to the samples to maintain the flexibility of the substrate. This explains the higher resistivity obtained when compared with gelatin composite films subjected to vacuum. Copper wires are then inserted throughout the sample at the places of the electrodes and wired to the multimeter. The specimen was then placed in a mechanical tester (Shimadzu, TeMeCo, Switzerland) mounted with a confined compression set-up.
Both strain and electrical resistance are recorded during the mechanical test. The values of the conductivity are calculated as described previously, taking into account the deformation of the electrodes.